Overview of the model
We provide simulations based on a CGE model. In this section, we explain the model and data used for the simulations. The structure of the model is basically the same as that of Takeda (2007), although we make some adjustments. Our model is relatively simple, but we cannot provide a full description of the model due to space limitations. For the algebraic representation of the model, see the supplementary material.Footnote 2
Our model is a single country model for Japan that divides the economy into 26 goods and 18 sectors, as listed in Table 1. Basically, one sector produces one good, but some sectors produce multiple goods, and some goods are produced by multiple sectors. For example, the “petroleum products” sector produces eight petroleum goods, and “electricity” is produced by multiple electricity sectors. Thus, the number of goods does not coincide with that of sectors. The model is a forward-looking dynamic model that covers the years 2011 to 2050. We treat five years as one period and solve the model for every five years to 2050. The model includes three types of agents: a representative household, firms and the government. We assume that all markets in the model are perfectly competitive and that all agents behave as price takers. The basic structure of the model is depicted in Fig. 1.
Table 1 List of goods and sectors Production side
Firms produce goods with constant-returns-to-scale technology using primary factors and intermediate inputs. The primary factors are labor, capital stock, land and resources. Land is a specific factor used only in the “agriculture, forestry and fishery” sector. Similarly, resources are specific to the “fossil fuels” and electricity sectors.Footnote 3
The production technology in each sector is represented by a constant elasticity of substitution (CES) production function. To consider the differences in the production technologies of goods and services with completely different properties, we divide the production sectors into the following five types: (1) general sectors, (2) “agriculture, forestry and fishery” sector, (3) “fossil fuels” sector, (4), electricity sectors, and (5) “petroleum products”, “coal products” and “gas and heat” sectors. The general sectors include all sectors not included in sectors 2–5. We assume different production functions for the different types of sectors. To specify the production functions, we mainly refer to the models used in the MIT EPPA model (Paltsev et al., 2005) and Takeda et al. (2010). Below, we explain the production structure of each sector.
First, the general sectors have the CES production function shown in Fig. 2. The tree diagram in the figure represents the structure of the nested CES function, where symbols, such as E_XX, indicate the elasticity of substitution (EOS) values between inputs. In the general sectors, output is produced by the Leontief aggregation of nonenergy intermediate inputs and an energy-primary factor composite (KLE). The energy-primary factor composite is a nested CES function of composite energy and primary factors (capital and labor). Composite energy is the CES aggregation of electricity and other energy composites, which is, in turn, the CES aggregation of all other energy goods. We use this type of nested production structure because we would like to consider the differences in the EOS values of various inputs.
Next, the production function of the “agriculture, forestry and fishery” sector is given by Fig. 3. In “agriculture, forestry and fishery” sector, the primary factor of land plays an important role in production. Thus, we assume a production function that emphasizes the role of land. In this sector, output is produced by the CES aggregation of land and nonland input, where land is the specific primary factor that is used only in this sector. The structure of nonland input is the same as the production tree of the general sectors. This production function implies that the output of this sector is strongly restricted by the amount of land.Footnote 4 The benchmark input data of land is derived from GTAP10 data.Footnote 5
The production function of the “fossil fuels” sector is basically the same as that of “agriculture, forestry and fishery” except that “resource” is used instead of land as a sector specific factor. The benchmark resource input data in the “fossil fuels” sector is also derived from the GTAP10 data.Footnote 6
The production function of the three electricity sectors has a structure similar to but slightly different from the “agriculture, forestry and fishery” and “fossil fuels” sectors. In the production function of the electricity sectors depicted in Fig. 4, the energy composite enters the second level Leontief nest as a nonenergy intermediate input. We assume this shape for the electricity sectors so that the energy input and the capital-labor composite cannot be substituted in electricity generation by fossil fuels. The electricity sectors use “resource” factors, which are also assumed to be specific to that sector. Although we call it “resource”, it does not represent natural resources but represents various nonmarket factors that affect production, and it is used as an instrument for controlling the production level.Footnote 7 The benchmark resource input data for the electricity sectors is derived by assuming that half of the original payment to capital is the payment to the resource input. For the nuclear and hydroelectricity sectors, we assume 0 for E_RES, which means that the amount of electricity produced by nuclear and hydro energy is basically controlled by the sector specific resource amount.
The “petroleum products”, “coal products” and “gas and heat” sectors have almost the same production function as the general sectors depicted in Fig. 2, but the method for treating the energy inputs is slightly different. For example, a large amount of “crude oil” is used in the “petroleum products” sector, but almost all of it is used as feedstock, which means that “crude oil” is used as a material. Thus, it is desirable to treat the oil input in the “petroleum products” sector as a nonenergy input. For this, “crude oil” enters the top Leontief nest in the “petroleum product” sector. A similar treatment is also applied to the “coal” used in the “coal product” sector and the “natural gas” and “LPG” used in the “gas and heat supply” sector.
The production functions explained above include many parameters, in particular, many EOS parameters. The values of the EOS parameters are provided later, in the “Parameters” section. Each sector determines the outputs and inputs needed to maximize their profits. The produced output is allocated to the domestic market or export market. The allocation is conducted through a constant elasticity of transformation (CET) function as in Lofgren et al. (2002) and Takeda (2007).
Demand side
To represent the demand side of the economy, we assume a microeconomic consumer household. This representative household’s utility depends on consumption and leisure. The utility during a period (hereafter, period utility) for the household is represented by the nested CES function in Fig. 5. Aggregate consumption is a CES aggregation of an energy composite and a nonenergy composite with an EOS of E_C. The energy composite is a CES aggregation of energy goods with an EOS of E_CE, and the nonenergy composite is a CES aggregation of nonenergy goods with an EOS of E_CNE. From the period utility in all periods, the lifetime utility of the household is derived as
$$\begin{array}{c}{u}^{L}={\left[{\sum }_{t=t0}^{T}{\alpha }_{t}^{u}{\left({u}_{t}^{P}\right)}^{\frac{\sigma -1}{\sigma }}\right]}^{\frac{\sigma }{\sigma -1}}\end{array}$$
(1)
where \({u}^{L}\) is the lifetime utility, \({u}_{t}^{P}\) is the period utility at period \(t\) and \(\sigma\) is the intertemporal elasticity of substitution; \(t0\) is the first period and \(T\) is the terminal period. The lifetime utility function in Eq. (1) is almost the same as those used in Bernstein et al. (1999), Takeda (2007) and Babiker et al. (2009).Footnote 8 The representative household chooses consumption and leisure subject to its lifetime budget constraint to maximize the lifetime utility.
Since the hours of leisure are equal to the total available time minus the hours of work, the leisure decision is equivalent to the labor supply decision. Similarly, since the total budget is allocated to consumption and savings, the consumption decision is equivalent to a savings decision. The representative household provides primary factors to the production sectors and obtains the factor income.
The dynamics of the model
Our model is a forward-looking dynamic model that assumes a household’s dynamic optimizing behavior. The dynamic structure of our model is based on Takeda (2007) except that we do not consider adjustment cost for investment.Footnote 9 Many CGE models used for the analysis of climate change policy, for example, the MIT EPPA model (Chen et al. 2015) and OECD ENV-Linkages model (Chateau et al. 2014), are dynamic models, but they are usually recursive dynamic models.Footnote 10 The recursive dynamic model is a kind of dynamic model that depicts the dynamic path of the economy by solving a myopic or static model iteratively.Footnote 11
An investment is intrinsically an intertemporal resource allocation and the current investment decision is based on the future returns from it. To incorporate this forward-looking nature of investment behavior into the model, we need the forward-looking dynamic model. In fact, macroeconomics, in which the decision regarding investment and saving is one of the main research themes, usually uses the forward-looking dynamic model.
On the other hand, recursive dynamic models (or static models) cannot capture the forward-looking investment behavior because they do not explicitly deal with future economic conditions. Actually, many recursive dynamic models determine investment (saving) by the assumption of a constant saving rate. Although some recursive dynamic models use more elaborate approaches, the recursive dynamic model can still only consider current or past economic conditions.
In this research, we assume that corporate tax is a tax on capital income, namely, a tax on return from investment. Therefore, the relationship between corporate tax and investment plays an important role. To capture this relationship appropriately, we employ the forward-looking dynamic model. With the forward-looking dynamic model, the decrease in the corporate tax rate in the future has the effect of stimulating the current investment. The recursive dynamic model or the static model cannot capture this intertemporal effect. This is why we adopt the forward-looking dynamic model.
The dynamic model in this paper is a deterministic model without uncertainty. Therefore, all agents in the model (especially, a representative household) determine their behavior with perfect foresights. When we solve the forward-looking dynamic model, we need to solve all periods simultaneously, which means that the model, particularly the multigoods, multisector model, includes a large number of variables. To reduce the number of variables included in the model, we set one period to five years and solve the model for every five years from 2011 to 2050.Footnote 12 Thus, the benchmark year is 2011 and the terminal year is 2050. Our model only covers periods until 2050 for the following reasons. First, the climate change policy after 2050 in Japan is not yet clear. Second, we have little information about the energy and carbon technology trends after 2050.
In solving a forward-looking dynamic model with a finite horizon, one problem arises. That is, if no condition is imposed on the terminal adjustment, investment becomes very low as the terminal period approaches because the capital stock existing after the terminal period is worthless. To avoid this problem, we adopt the approach used in Lau et al. (2002). More specifically, we impose the following condition
$$\frac{in{v}_{T}}{in{v}_{T-1}}=\frac{{c}_{T}}{{c}_{T-1}}$$
where \(in{v}_{t}\) is the investment in period \(t\), \({c}_{t}\) is the consumption in period \(t\) and \(T\) is the terminal period. This condition implies that the rate of increase in investment in the terminal period is equal to that of consumption. With this condition, investment near the terminal period will behave smoothly, as in an infinite horizon model. The same approach is used in Bernstein et al. (1999), Takeda (2007) and Babiker et al. (2009).
As Takeda et al. (2010), we assume that the annual depreciation rate for capital is 7%. In addition, we assume that the total time available for the representative household decreases over time at the annual rate of 0.4%.Footnote 13 Similarly, we assume that the amount of endowments of land and sector specific resources are kept constant over time. By this assumption, the amount of electricity generated by nuclear and hydro energies is kept constant over time. The supply of electricity by hydro energy is strongly constrained by geographical conditions, and it is unlikely that hydro power will change significantly in Japan in the future. With respect to nuclear power in Japan, there is great uncertainty regarding its future use, but the current Japanese government plans to use a certain amount of nuclear as of 2030. Taking account of these situations, we assume that the amount of nuclear and hydro power is constant at the benchmark value over time.
Since our model covers a long time span, the change in technology plays an important role in determining the impacts of climate change policy. For this, we consider growth in total factor productivity (TFP) and autonomous energy efficiency improvement (AEEI). The TFP growth rate and AEEI rate will be explained in the “Simulation scenarios” section.
Government
The government collects revenue from consumption taxes, income taxes, corporate taxes and other taxes. Then, the government uses this revenue to finance government consumption. We assume that government consumption is constant at the benchmark value over time.
In the environmental tax reform simulation presented later, we reduce the rates of income tax, corporate tax and consumption tax with the introduction of a carbon tax. Thus, these three taxes are of great importance for our analysis. Although there are other various taxes in Japan, we focus on these three taxes because they are main taxes in Japan tax system.Footnote 14 In this section, we explain how these three taxes are incorporated into the model.
First, the income tax is incorporated into the model as a tax on the labor income of the household. Second, the corporate tax is assumed to be a tax on the return from investment (capital stock). Finally, the consumption tax, as its name implies, is a tax on consumption. For all taxes, we derive the benchmark tax rate by dividing tax payments by the tax base in the benchmark year. For example, the benchmark income tax rate is derived according to the following formula: income tax rate = value of income tax/value of labor income. This means that all the tax rates in our model are average tax rates. For tax data in the benchmark year 2011, we use the data in “Ministry of Finance statistics monthly No. 722” (Policy Research Institute 2012).Footnote 15 The derived benchmark tax rates for income tax, corporate tax and consumption tax are 5.7%, 4.9% and 3.6%, respectively. Note that the derived consumption tax rate is lower than the actual rate (the consumption tax rate in 2011 was 5% in Japan). There are many possible reasons for this discrepancy, for example, some goods and service are exempt from the consumption tax.Footnote 16 The fact that the tax rates of income tax, corporate tax and consumption tax are derived from the tax data of Japan means that the taxes in our model are not just numerical examples but reflect the actual Japanese tax system.Footnote 17 All the tax rates in the model are kept constant in the simulation except when we consider environmental tax reform.Footnote 18
International trade
Our model focuses only on Japan, but we need to consider international trade in goods and services. To incorporate international trade, as in Takeda (2007), we assume that Japan is a small country, which means that the terms of trade in Japan are constant. We assume that the foreign exchange rate is adjusted so that the trade balance is kept constant at the benchmark level.Footnote 19 As with other CGE models, we use the Armington assumption (Armington 1969), which means that domestic goods and imported goods are imperfect substitutes and are aggregated through a CES function.
Carbon tax
In the later simulation, we use a carbon tax to regulate CO2 emissions. The carbon tax is a tax based on the amount of CO2 from fossil fuels. Thus, let \({p}_{i}\) be the original price of fossil fuel \(i\), \({t}^{\mathrm{CO}2}\) be the carbon tax rate, and \({\delta }_{i}\) be the carbon coefficient (the amount of CO2 per unit of fossil fuel \(i\)). Then, the user price of fossil fuel is given byFootnote 20
$${p}_{i}^{A}={p}_{i}+{t}^{CO2}{\delta }_{i}$$
In the simulation, we set the path of CO2 emissions exogenously, and the carbon tax rate is determined endogenously so that the CO2 emissions derived from the model are equal to the target level. This means that carbon tax level changes over time. More specifically, as the reduction rate in CO2 increases over time, the required level of carbon tax also increases. We assume the exogenous path of CO2 emissions because the climate change policy in Japan usually uses the CO2 emissions level as the policy target. The introduction of a carbon tax generates additional tax revenue. The use of a carbon tax revenue is discussed in a later section.
Renewable energy and CCS
New technology and energy play important roles in the long-term analysis of climate change policy. Specifically, as explained in the introduction, renewable energy and CCS are regarded as essential policy measures to mitigate climate change. Thus, we incorporate these two factors into our model.
First, in addition to electricity generated by conventional energy (fossil fuel, nuclear and hydropower), we add the electricity generated by renewable energy. Like the conventional electricity sectors, this renewable electricity sector generates electricity using various production inputs, but fossil fuels are not used and, thus, CO2 is not emitted.
Figure 6 shows the production function of the renewable energy electricity sector. Since there is no information regarding the production structure of this sector in the benchmark data (input–output table), we must specify the production function by other data. To specify the production function, we use benchmark the “input cost share” data and “markup factor”. The benchmark input cost share indicates the benchmark share of each input in the total cost. The markup factor specifies the cost of the renewable energy electricity relative to the existing technology. We use this information to specify the production function of the renewable energy electricity sector. The same approach is used in, for example, Takeda et al. (2010) and the MIT EPPA model (Paltsev et al. 2005).
We can obtain the benchmark input cost share data from the estimates provided by the Power Generation Cost Verification Working Group.Footnote 21 For example, in the total cost of generating electricity by solar power, “policy cost”, “operating cost including labor cost”, and “capital cost” account for 13.6%, 12.4% and 74.0%, respectively.Footnote 22 Since the classification of inputs used in the above estimate does not match the classification of goods in our model, we cannot use the estimate directly in our model. However, we do not have another appropriate estimate. Therefore, from this estimate, we assume the benchmark cost share of inputs for the renewable energy electricity sector of our model as follows: “other services” = 10%, “labor” = 10%, “capital” = 40, “resource” = 40%. As in the conventional electricity sectors, we assume a sector specific resource input, which is used as the factor controlling the supply of electricity by renewable energies.
In addition, we need to determine the values of the markup factor and the amount of the sector specific resource factor. To do so, we use the World Energy Outlook (WEO) 2018 (International Energy Agency 2018). More specifically, we determine the values of two parameters so that the supply of electricity from renewable energies is close to the value predicted in WEO 2018.Footnote 23
Since we assume that the cost of electricity generated by renewables is higher than that of the conventional electricity sectors (that is, the markup factor is assumed to be high), the supply of electricity generated by renewables is small in the early period and increases gradually as the CO2 regulation is strengthened and the price of electricity rises. Because there is huge uncertainty in the cost and limit of renewable energy, we conduct the sensitivity analysis of the assumption regarding the amount of renewable energy.
Next, we explain the approach for modeling the CCS activity. CCS is usually combined with coal-fired electricity generation, but for simplicity, we assume that the CCS activity is conducted by an independent sector. The production function of the CCS sector is given by Fig. 7, which shows that the CCS activity is supplied under the Leontief production function with fixed coefficients. Since we have no appropriate information for specifying the parameters in the production function, we use the cost share information of the renewable energy electricity sector for the CCS activity, although this approach is slightly ad hoc. We assume that the sector specific resource input and other inputs are not substitutable because the CCS activity is likely to be strongly restricted by the technological and geographical factors that are embodied in the sector specific resource factor.
We adjust the markup factor so that cost of CCS is close to 10,000 yen per ton, which is taken from the report published by Ministry of the Environment.Footnote 24 This relatively high cost of CCS means that CCS is not supplied in the early periods and the supply of CCS increases as the carbon price rises. We adjust the amount of the sector specific resource so that an upper limit on CCS becomes 180 MtCO2 per year, which is taken from the estimate by Akimoto and Sano (2017).
Because there is huge uncertainty about the available amount of CCS, we conduct the sensitivity analysis on the amount of CCS. The existence of CCS means that net CO2 emissions are equal to gross CO2 emissions minus CCS.
Benchmark data
Any CGE analysis is based on the benchmark data that represent the economy at a certain period. We use Japanese input–output data from 2011 (Ministry of Internal Affairs and Communications Japan 2016) for the benchmark data and aggregate sectors and goods of the original IO data into the sectors and goods in Table 1. For CO2 emissions data, we use 3EID data from 2011 (Center for Global Environmental Research 2018).
Parameters
The functions appearing in the model include many parameters. The values of the EOS parameters are reported in Table 2, where the symbols indicate the EOS parameters appearing in the figures and the text. The column “Source” indicates the source from which the parameter values are taken. The EOS values are basically taken from the previous CGE studies, but we change some of them slightly to fit our model. Because we have no empirical estimate for E_LND, we assume 0.5.
Table 2 Value of elasticity of substitution parameters